Kerry, some of your assumptions here are all wet.
I am reminded of a PLB story from a couple of years ago that I related here. A backpacking group was a few days out from Rock Creek on the east side of the Sierra Nevada, so they had crossed onto the west side. One gal got very sick from altitude, and she tried to keep struggling ahead. Finally she was near collapse, so a camp was made and the group tried to support her. A runner was sent out toward the east side to get help. Meanwhile, a stranger with a Spot device was nearby. The decision was made to push the button. Once that was done, the stranger didn't feel that it was necessary for him to remain on the site, so he took off up the trail. Apparently the signal was received and there was a helicopter dispatched from the Fresno County sheriff's office to go to the transmitted GPS coordinates. However, the sheriff's office saw that the Spot location was moving up the trail. The Spot user didn't realize that once it is activated, it is locked on, and you must remain at the emergency site. When the sheriff's office saw that the Spot was moving, they assumed that it had been a false alarm, so they recalled the helicopter. As a result, no helicopter arrived. Meanwhile, the runner reached a telephone on the east side, and that call got routed to the Fresno office on the west side. They put two and two together and figured out that an emergency was still present, so they dispatched the helicopter again. A small helicopter reached the location and the sick gal was loaded into it. However, due to the size of the aircraft, there was no room for anything except the pilot, the sick gal, no equipment, and no medic.
Strangely and incidentally, the helicopter ride was short. They flew her to VVR and dropped her off with wet clothing and no gear. She had to get a vehicle ride down to Fresno from there. (bizarre!)
Now, if there had been some good two-way communications, the dispatcher could have found out the nature of the emergency and the urgency of it.
So, your comment, "The team that shows up is going to be equipped to handle any emergency they encounter, medical or otherwise..." is just a bunch of crap.